The family of an Angolan man who collapsed and died on a passenger plane as he was being removed from the UK are calling for a parliamentary inquiry into "systematic problems" with the deportation system.

Senior officials from G4S, the company used by the government to remove detainees, will be questioned by MPs on the home affairs committee tomorrow over "concerns" about the rules governing removals from the UK and their enforcement.

Three G4S guards have been arrested by police investigating the death of Jimmy Mubenga, 46, who collapsed on a British Airways flight that was preparing to fly from Heathrow last month.

According to passengers on the aircraft who spoke to the Guardian, Mubenga was being heavily restrained and was complaining of breathing difficulties prior to losing consciousness.

Mubenga's family said tonight they would be writing to the select committee to request an inquiry into the wider issues raised by the case. Speaking through their solicitor, they said that while it was up to the police to investigate his death, the case raised wider questions about the way deportees were treated.

"We urge the committee to begin an inquiry into the wider, potentially systematic problems at the heart of the deportation system to ensure there are no further tragedies of this kind."

The request has been backed by Inquest, a campaign group that advises families of people who die in custody.

G4S, the world's largest security firm, said it was "extremely disappointed" last week to lose the lucrative government contract to forcibly deport people.

Damian Green, the immigration minister, told parliament today the decision to award the contract to a rival firm, Reliance Security Task Management Limited, had been taken in August and had "nothing to do with recent events".

Later a Home Office spokesman clarified his remarks, stating that Reliance had been identified as a lead bidder over the summer, but the decision to give the company the contract over G4S was not "ratified" until last week.

David Banks, group managing director for G4S, and Stephen Small, managing director for the firm's detention and escorting contract, are likely to be pressed over allegations of safety breaches by G4S guards when they give evidence to the select committee.Nick Buckles, the chief executive of G4S, recently told the BBC: "We have 625,000 staff and we have incidents that occur fairly regularly in our business. This is a very tragic incident that we are dealing with. We still haven't seen the outcome of the postmortem but we're obviously very sad for the family, and sad for our employees as well."

Buckles said guards received eight weeks training to ensure "they are well-qualified in restraint and other techniques".

The Guardian has provided the committee chair, Keith Vaz, with a document showing G4S was warned in March 2006 that restraint techniques being used by its guards were potentially lethal. The letter was headed "positional asphyxia" – a form of suffocation caused when people are placed in dangerous restraint holds – and was circulated to all G4S staff after the Home Office witnessed them using an unauthorised form of restraint.

There are currently three Metropolitan police investigations into allegations of mistreatment by G4S guards this year.

The two cases relating to potentially problematic restraint holds include that of Mubenga and another man, Ludovic Paykong, who was deported to Cameroon in March. He claims he temporarily lost consciousness when guards "used considerable force to shut my mouth to stop me from shouting and hold my head in place".